A fiber placement machine includes a movable wrist with a fiber placement head at one end of the wrist. A roller system for delivering fibers to the fiber placement head includes a J-axis roller located spaced from the ends of the wrist, a K-axis roller at the end of the wrist that supports the head, and an A-axis roller at the opposite end of the wrist. The axis of the K-axis rollers swivel depending on the rotation of the head, and the A-axis rollers swivel as a function of the swiveling of the K-axis rollers. As the A-axis rollers swivel, at least one end of the A-axis roller is displaced toward the J-axis roller to maintain a constant path length for the fiber tows between the A-axis roller and the J-axis roller.